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Nodal analysis Confusion

  1. Aug 9, 2012 #1
    In nodal analysis method, two books use different and contradicting approaches and not sure which one is correct. One books says that currents at each nodes should be treated independently from the other nodes so that the same current can have two opposing directions in the same equations. The other book uses the opposite method, where the current direction is consistent which makes more sense. Which one is correct?
  2. jcsd
  3. Aug 9, 2012 #2
    It turns out it doesn't matter in the end how you define current direction (the signs will cancel). It is arbitrary (since it is an unknown) and the equations all work out as long as you are CONSISTENT. I would follow the method that makes more sense to you. For kicks, you can try solving a simple circuit using both methods and you will see they agree.
  4. Aug 9, 2012 #3
    x2. They are both the same thing. If you try a very simple circuit that requires nodal analysis you will notice that they both turn out the same at the end.
  5. Aug 10, 2012 #4
    Should I assume element voltage polarity arbitrarily and independently of the assumed current direction through the same element?

    And when doing nodal analysis, since current direction consistency does not matter, what about element polarity? Can I assume different ones when working on a different node?

  6. Aug 10, 2012 #5
    Here you have two more examples:



    For this circuit from KCL

    I3 = I1 + I2

    (Va - 4V)/6Ω = (10V - Va)/10Ω + (6V - Va)/4Ω

    And after solve this I get

    Va -> 190/31 = 6.12903226V



    And again form KCL

    (-I1) + (-I2) + (-I3) = 0


    - I1 - I2 - I3 = 0

    So know all current flow outward (away) from the node.
    So this assume that voltage at node Va should be at higher potential.
    And current flow from + to - , I assume that if current entering into a node I give him " +"
    and current that come out form the node I give "-".
    But you can choose whatever you wont but you must be consistent in your choice

    So I can write:

    -(Va - 10V)/10Ω - (Va - 6V)/4Ω - (Va - 4V)/6Ω = 0

    And again the answer is exactly the same

    Va -> 190/31 = 6.12903226V

    And maybe another example for this diagram I choose

    But I also can assume that if current flow out from the node I give a "+" sign.

    I1 + I2 + I3 = 0 ( no current entering the node).
    Since all current flow out from the node the Va node should be at higher potential.

    (Va - 10V)/10Ω + (Va - 6V)/4Ω + (Va - 4V)/6Ω = 0

    And the answer is
    Va -> 190/31 = 6.12903226V
    What a surprise
  7. Aug 10, 2012 #6
    Thanks a lot!

    After reading your example, I tried a different one and this time using at each node different directions for the same current. It worked like a charm! the trick is consistency in applying the sign convention.
  8. Aug 10, 2012 #7
    Any idea why NILSSON & RIEDEL book is very popular in academia while it's nothing compared to Sudoki & Alexander?
  9. Aug 10, 2012 #8
    No idea. I used Nilsson and Riedel in school...

    Wait till you get to Johns and Martin to see how people REALLY design circuits.
  10. Aug 10, 2012 #9
    I mean for basic material I would choose something that teaches readers instead of just talking to them or even to itself. Maybe they like the names, sound more academic :D
    Nilsson and Riedel!
  11. Aug 11, 2012 #10
  12. Aug 11, 2012 #11
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